Wasserstein barycenter was initially introduced by [1]}. Given probability measures \(\mathcal {R}_1, ..., \mathcal {R}_l \in S_2(\theta )\)  for \(l \ge 1\) , their Wasserstein barycenter \(\tilde{\mathcal {R}}_{l,\mu }\)  is defined as follows:
\(\tilde{\mathcal {R}}_{l,\mu }=\underset{\mathcal {R} \in S_2(\theta )}{\mathrm {argmin}}\sum _{i=1}^l \mu _i W_2^2(\mathcal {R},\mathcal {R}_i),\) 
